Does anyone know if there is a limit to the number of remotes some garage door openers will accept? I ask because we got a third car, programmed the Homelink, and the one in my car no longer worked. Reprogrammed mine, and the one in the new car no longer worked.

So right now, besides the remotes that came with the door, we have three other remotes programmed - two Homelink systems in cars, one keypad wireless remote outside. Is that the limit?